In an interview with CBS, Pompeo was asked if the US had "any insight" regarding the bombings in Sri Lanka.
"Every indication is that this was at the very least inspired by ISIS," Pompeo answered.
He added that there would be more information about whether there were "actual connections."
"The scale, the complexity of the attack certainly would be something a good analyst like yourself would stare at and say, 'We need to dig really hard.' The capacity for a local group to pull off a relatively complex, simultaneous attack, it could happen. But it's probably the case that there were others assisting them," Pompeo told CBS News Senior National Security Analyst and former CIA Acting Director Michael Morell.
During the interview, Pompeo noted that Daesh* and other terrorist groups would remain threats to the US' security and that the US would "continue to stay right on top" of taking down terrorist networks.
"Even apart from the Sri Lanka incident, it's absolutely the case that the capacity for ISIS and other radical Islamic terror groups, Sunni terror groups remains," Pompeo said. "We have Al-Qaeda in the Arabian Peninsula that still has real capacity to put the United States at risk through its expertise. There are lots of pockets we could walk through. But this challenge of taking down these networks is something the United States is going to have to continue to stay right on top of."
Pompeo's statements appeared to be a part of a CBS "Intelligence Matters" interview which is to be released on 1 May.
A massive security operation was launched following the attacks. Sri Lankan authorities introduced and re-introduced curfews, deploying an extra 1,000 troops in the capital of Colombo.
Daesh has reportedly claimed responsibility for the Sri Lanka attacks and released images that purported to depict the attackers. Prime Minister Ranil Wickremesinghe said that investigators were still determining the extent of the bombers' foreign links, Reuters reported.
* Daesh (ISIL/ISIS/IS/the Islamic State), Al-Nusra Front, Hayat Tahrir al-Sham are terrorist groups banned in Russia and many other countries.